Numerical inference of the molecular origin of the cyanobacterial circadian rhythm

The cyanobacterial clock proteins, KaiA, KaiB, and KaiC, are known as the simplest biological clock; Just by mixing them with ATP in a test tube, self-sustaining oscillation with a nearly 24h temperature-compensated period is reconstituted. To elucidate the molecular mechanisms of this oscillator, experimental studies have revealed and investigated in detail various elementary reactions/processes, ranging from local chemical reactions of ligands to global (dis)assembly of the proteins. Yet, proposing molecularly detailed mechanisms of the clock functions is still difficult because almost all experimentally measurable quantities are the results of complicated interplays between many elementary processes, i.e. independent measurement of an elementary process is difficult. In this talk, I will present a numerical approach to obtain the rate constants of the elementary processes from experimental data [1, 2]. First, a reaction model consisting of rate equations of the elementary processes is built. Then, their rate constants and temperature dependence are inferred by simultaneously fitting model outputs to multiple types of experimental data (such as phosphorylation reactions and ATPase activity) at various temperatures. On the basis of the inferred parameter values, we can quantitatively discuss how the clock functions arise from the interplays between elementary processes. As an example, I will present a potential molecular mechanism of the temperature compensation of period.